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Python for Finance

Python for Finance

By : Yuxing Yan
3.9 (22)
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Python for Finance

Python for Finance

3.9 (22)
By: Yuxing Yan

Overview of this book

A hands-on guide with easy-to-follow examples to help you learn about option theory, quantitative finance, financial modeling, and time series using Python. Python for Finance is perfect for graduate students, practitioners, and application developers who wish to learn how to utilize Python to handle their financial needs. Basic knowledge of Python will be helpful but knowledge of programming is necessary.
Table of Contents (14 chapters)
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13
Index

The GARCH (Generalized ARCH) model

Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is an important extension of ARCH, by Bollerslev (1986). The GARCH (p,q) process is defined as follows:

The GARCH (Generalized ARCH) model

Here, The GARCH (Generalized ARCH) model is the variance at time t, q is the order for the error terms, p is the order for the variance, The GARCH (Generalized ARCH) model is a constant, The GARCH (Generalized ARCH) model is the coefficient for the error term at t-i, The GARCH (Generalized ARCH) model is the coefficient for the variance at time t-i. Obviously, the simplest GARCH process is when both p and q are set to 1, that is, GARCH (1,1), which has following formula:

The GARCH (Generalized ARCH) model

Simulating a GARCH process

Based on the previous program related to ARCH (1), we could simulate a GARCH (1,1) process as follows:

import scipy as sp
sp.random.seed(12345)
n=1000          # n is the number of observations
n1=100          # we need to drop the first several observations
n2=n+n1         # sum of two numbers
alpha=(0.1,0.3)     # GARCH (1,1) coefficients alpha0 and alpha1, see Equation (3)
beta=0.2
errors=sp.random.normal(0,1,n2)
t=sp.zeros(n2...

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